Problem: Solve for $x$, ignoring any extraneous solutions: $\dfrac{x^2}{x + 7} = \dfrac{x + 56}{x + 7}$
Answer: Multiply both sides by $x + 7$ $ \dfrac{x^2}{x + 7} (x + 7) = \dfrac{x + 56}{x + 7} (x + 7)$ $ x^2 = x + 56$ Subtract $x + 56$ from both sides: $ x^2 - (x + 56) = x + 56 - (x + 56)$ $ x^2 - x - 56 = 0$ Factor the expression: $ (x + 7)(x - 8) = 0$ Therefore $x = -7$ or $x = 8$ However, the original expression is undefined when $x = -7$. Therefore, the only solution is $x = 8$.